Learning Lineage-guided Geodesics with Finsler Geometry

TL;DR

This paper introduces a Finsler metric that integrates geometric and prior classification information to improve trajectory inference in dynamical systems, especially when lineage or transition priors are available.

Contribution

It proposes a novel Finsler geometry-based approach that combines spatial features with discrete prior knowledge for enhanced trajectory interpolation.

Findings

Improved interpolation accuracy on synthetic data

Enhanced performance on real-world biological data

Effective integration of lineage priors in trajectory inference

Abstract

Trajectory inference investigates how to interpolate paths between observed timepoints of dynamical systems, such as temporally resolved population distributions, with the goal of inferring trajectories at unseen times and better understanding system dynamics. Previous work has focused on continuous geometric priors, utilizing data-dependent spatial features to define a Riemannian metric. In many applications, there exists discrete, directed prior knowledge over admissible transitions (e.g. lineage trees in developmental biology). We introduce a Finsler metric that combines geometry with classification and incorporate both types of priors in trajectory inference, yielding improved performance on interpolation tasks in synthetic and real-world data.